Traction Motor Retarding Flux Reference

ABSTRACT

A traction motor system calculates motor flux by generating a real time effective resistance of a resistance grid calculated from motor torque and measured voltage on a DC link. Calculating effective resistance avoids solely relying on DC link voltage, which can be influenced by conditions such as wheel slip and drop out of one or more resistance grids. The effective resistance calculation is based on nominal motor values using known power levels and conditions. From these nominal values and the effective resistance, various scaling factors based on actual motor power can be generated and used to adjust a nominal flux reference to more accurately reflect actual motor flux. The scaling factors include power and torque scaling factors and a resistance scaling factor that is active during conditions such as wheel slip.

TECHNICAL FIELD

The present disclosure generally relates to electric drive motors andparticularly to flux estimation in electric drive motors during brakingoperation.

BACKGROUND

Operation of traction motors, for example, in a railroad locomotive,involves several layers of control for both propel (drive) operation andretard (brake) operation. For example, while an operator may adjust athrottle, an upper level controller may call for acceleration ordeceleration, and a lower level controller may adjust torque based onthe call for acceleration or deceleration. Even though the relationshipsare easily calculated in an ideal case, implementation of control at thegiven levels may require different data related to the drive systemoperating environment in order to carry out the necessary controls. Forexample, when managing torque in an AC traction motor, knowledge ofmotor flux is necessary for properly controlling inverters that setmotor voltage and phase. In an ideal condition, DC link (supply) voltagecan be used to estimate flux. However, many real world conditions,including wheel slip and resistive grid drop out, contribute to changesin link voltage that can lead to substantial errors in flux calculation.

A typical vehicle AC drive system may include several tractioninverters, each driving one or more motors, all connected to a common DClink. When the motors are operated in retarding modes, power is fed fromthe motors into the DC link and the generated power is commonlydissipated in a resistive grid. The DC link voltage in this mode ofoperation is related to the total power produced by all inverters/motorsas they feed that power into the resistive grid. In general, this meansthat a higher torque or power produced by one inverter/motor willincrease the DC link voltage, however there is not always a one-to-onerelationship of each inverter's contribution to the net DC link voltagedue a lack of consistency among other inverters that are also connectedto the DC link. In order to maintain desired efficiency and torqueaccuracy, there is a requirement to accurately set the traction motorflux reference in retarding modes of operation. This flux reference canthen be used in typical vector-control methods to set current andvoltage targets for motor control. Ideally, this flux reference willvary with DC link voltage (among other inputs) in order to maximize theflux and therefore the efficiency.

Typically the flux reference is set based on a measurement of the DClink voltage. Particularly during braking, the flux reference affectsquadrature axis current Iq, which in turn affects torque. Torque affectspower and power affects DC link voltage. This circular path can lead tooscillations and instability as the reference will necessarily lagbehind the measurement, causing differences between the actual flux andthe flux reference.

Another approach is to set the flux reference based on the invertertorque reference. In a single-inverter system this will work well, butin a system where multiple inverters can operate at varying power levelson a common DC link the lack of a one-to-one relationship between torqueand voltage makes this approach problematic.

It is necessary to develop a flux reference more indirectly so that thelack of information and inherent instability in traditional measurementscan be avoided while responding correctly to torque requirements.

SUMMARY OF THE DISCLOSURE

In one aspect of the current disclosure, a method of adjustingelectrical power application in a motor control system using an AC motordriven by an inverter bank that is coupled to a resistive grid duringretard operation includes calculating a braking factor as a ratio of anominal power DC voltage vs. a nominal brake DC voltage, calculating aresistance scale factor as a ratio of measured grid resistance vs. abase grid resistance and determining that motor operation is in one of aconstant power region or a constant torque region. The method mayfurther include multiplying a DC link voltage, the braking factor, theresistance scale factor and one of a power scale factor when in aconstant power region or a torque scale factor when in a constant torqueregion to generate an adjusted flux estimate and setting inverteroperation to adjust motor torque based on the adjusted flux estimate,where the power scale factor is a function of a measured torque timesmechanical frequency vs. a characteristic torque times a corner pointmechanical frequency and the torque scale factor is a function of themeasured torque vs. the characteristic torque.

In another aspect of the current disclosure, another method of operatingan AC motor driven by an inverter includes determining a base resistanceconstant using characteristics of the motor at a first motor rotationfrequency, where the first motor rotation frequency defined at atransition point between constant torque operation of the motor andconstant power operation of the motor (“the knee frequency.” The methodmay also include calculating motor power as a function of the actualtorque and the actual motor rotation frequency, calculating an effectiveresistance at the inverter as a function of motor power and a voltage onthe DC link and calculating an estimated flux reference as a function ofthe DC link voltage, the effective resistance, and the base resistanceconstant. The method may also include adjusting torque output of themotor based on the estimated flux reference.

In yet another aspect of the current disclosure, an alternating current(AC) motor system adapted to adjust motor flux based on motor power, adirect current (DC) link voltage, and an effective resistance at aninverter used to drive the AC motor may include an AC generator, arectifier that converts an output of the generator to DC power, a DClink coupled to the rectifier, a resistive grid selectively coupled tothe DC link,

A plurality of AC motors and a plurality of inverters, each of theplurality of inverters electrically coupling the DC link to a respectiveone AC motor of the plurality of AC motors. the system may also includea controller coupled to the DC link, the resistive grid, and each of theplurality of inverters, the controller itself including a processor anda memory that stores instructions that when executed on the processorcause the controller to i) calculate an estimated flux based at least inpart on an effective resistance of the grid at each inverter of theplurality of inverters, where the effective resistance is calculatedfrom actual torque, actual motor rotation frequency, the DC link voltageand a base resistance constant and ii) adjust a setting for eachinverter of the plurality of inverters that controls a torque of the ACmotor associated with each inverter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an AC motor drive system;

FIG. 2 is a graph of an exemplary motor power vs. speed curve; and

FIG. 3 is a flowchart of an exemplary method operating an AC motordriven by an inverter.

DETAILED DESCRIPTION

AC motor drive systems, such as those used in locomotives, use invertersto generate specialized stator waveforms in a direct axis (d current, orId) and a quadrature axis (q current, or Iq) to control motor torque.When operated in a drive or propel mode energy from a DC link is appliedto the motor. When used in a brake or retard mode energy generated bythe motor may be dissipated in a resistive grid. In other alternatives,the energy from brake mode operation may be recovered in a battery orcapacitor.

Generally, at other than peak drive or brake operation, the invertereffectively isolates its respective motor from the DC link. However,when at maximum power situations, the ratio between DC voltage and motorvoltage, known as modulation ratio, is set to its maximum value and thevoltage applied to the motor varies directly with the DC link voltage.Correspondingly, motor flux also varies directly with DC link voltage.As result, even though the controller managing the inverter cannotcontrol the flux, it is still necessary to have a good estimate of theactual flux so that the Iq current references are accurate and torqueproduction can be correctly managed.

As discussed in detail below, a flux reference may be developed using acombination of feed-forward and feedback terms based on knowncharacteristics of the motor and measurements available to thecontroller.

FIG. 1 is a schematic of an AC motor drive system 10 suitable for use inimplementing the flux estimation and motor management techniquesdisclosed. While the discussion following is in terms of a multi-axle ora multi-bogie locomotive, other applications where inverter-drivenmotors share a common DC link may benefit from this system and method.

The system 10 may include a generator 12 that provides AC power to arectifier 14 that, in turn, generates DC power on the DC link 16. Eachof a plurality of inverters 18 are coupled to the DC link 16. In apropel mode, the inverters 18 may generate three phase power to theirrespective motors 20 by adjusting voltage and/or phase voltage availableon the DC link 16 to a respective motor phase, in a known manner. In aretard mode, or brake mode, each of the inverters 18 may return powergenerated by its respective motor 20 to the DC link 16, which may bedissipated in a resistive grid 26 common to each of the inverters 18. Insome embodiments, each of the inverters 18 may have a separate resistivegrid (not depicted).

In the case of an axle-control locomotive, there are generally sixinverter-motor sets, each set driving one axle. In other embodiments, alocomotive may have fewer or more axles. In general, all the inverters18 are coupled to the DC link 16 in common, as well as to the resistivegrid 26 which may be selectively switched in or out via switches 28under the direction of a controller 30. Special cases, particularly inthat of bogie-control configurations are discussed further below. Thecontroller 30 may include a memory 32 and a processor 34. The controller30 may also include inputs 36, 38 from the DC link 16, a control output40 to the grid switches 28, and control lines 42, 44 to each individualinverter of the plurality of inverters 18. The control lines 42, 44 mayalso include sensing feedback from the inverters for use in determininga state of each inverter, such as a back electromotive force (EMF) onthe motor phases.

The controller 30 may be responsive to a higher level control system 46,such as a cab control used by an operator/engineer or an intermediatecontroller that translates a change in throttle position into a requestfor acceleration or deceleration or power, that may, in turn, betranslated into a torque requirement at the controller 30. In someembodiments, the controller 30 may be physically implemented asindividual controllers (not depicted), each controlling one inverter.

The memory 32 may be any combination of volatile and non-volatilememory, including rotating media, flash memory, conventional RAM, ROM orother non-volatile programmable memory, but does not include carrierwaves or other propagated media.

The memory 32 may include storage for various aspects of operation ofthe controller 30 including various modules implementing an operatingsystem, utilities, and operational programs, as well as short-term andlong-term storage for various settings and variables used duringoperation.

The processor 34 may be any of a number of known computer processorarchitectures, including, but not limited to, single chip processors orconventional computer architectures.

In operation, when the locomotive is in propel mode, the DC link voltageis a function of the generator 12 and power on the DC link 16 istransferred to an individual motor 24 of the plurality of motors 20 viaits respective inverter 22 of the plurality of inverters 18. Conversely,in brake mode, the motors 20 supply power via their respective inverters18. During braking the, switches 28 are closed and in one embodiment,the power generated by the motors 20 is dissipated in the resistive grid26. In braking mode, the voltage on the DC link is a function of theresistive grid and the current being output by the plurality ofinverters 18. In either mode, it is important that the controller 30have a flux reference that matches the actual motor flux because motortorque is the only setting of interest at this level of control andtorque is a direct function of flux.

When a motor 24 is operating outside the “one-pulse” region, the motorvoltage (the voltage between the inverter and motor) is some fraction ofthe DC link voltage based on a modulation ratio, allowing the inverter22 to maintain a constant voltage at the motor 24 even with variationsof the DC link voltage. However, when operating in the “one pulse”region, each inverter's modulation ratio is set to 1 and the voltage onthe DC link 16 is passed directly to each of the motors 20. Therefore,there is no ability to correct for changes in DC link voltage due toload variations, generator speed, etc. Similarly, in braking mode,because the resistive grid has a fixed resistance, the DC link voltageis purely a function of the power output of the plurality of motors 20.Even though in this one-pulse region, the controller 30 cannot controlmotor flux, it is still necessary to have a good estimate of the actualflux so that calculations of the q-axis current reference are accurate,leading to accurate torque production.

During nominal one-pulse operation, each inverter-motor set operatesvirtually identically and the estimation of motor flux directlycorrelates to the voltage on the DC link 16. However, even in thisnominal situation simply using DC link voltage for flux estimation hasseveral problems. First, particularly during braking, the DC linkvoltage is directly related to the power created by the motors 20, whichis directly related to the flux estimate which is used to calculate Iq,which affects torque, which by affecting power completes a control loopfor DC link voltage. Because there are delays in this control loop,using the DC link voltage may lead to oscillation and instability.Second, several conditions may occur that further complicate the soleuse of DC link voltage in creating a flux estimate.

One condition affecting DC link voltage is wheel slip, where thephysical locomotive wheels slip on the tracks, causing, during braking,the motor to change speed and produce less power than the other motors.This unequal loading alters the DC link voltage unpredictably so thatthe relationship between DC link voltage and motor flux that isavailable during nominal operation is no longer valid.

Another condition affecting DC link voltage is inverter cut out. In somecases, either by design or due to failure, one or more inverters 18 maybe turned off, also resulting in the original relationship between DClink voltage and motor flux to no longer be valid because the number ofinverter-motors participating in the system 10 has changed.

A combination of feed-forward and feedback terms may be used to reduceinstabilities caused by loop delays in the DC link 16 and to account forconditions such as wheel slip and inverter cut out. A valuablerelationship between current, voltage, and power and the definition offlux linkage may be used to generate both the feed-forward and feedbackterms.

In the following discussion, variables are defined as:

T_(ε8)=torque of the motor at throttle level 8,

T_(ε)=torque of the motor

T_(DB8)=torque of the motor during dynamic braking at throttle level 8

ω_(mc)=mechanical frequency of the motor at a knee frequency defined ata transition point between constant torque operation of the motor andconstant power operation of the motor

ω_(m)=mechanical frequency of the motor

V_(DC) _(—) _(TH8)=DC link voltage in propel mode at throttle level 8

V_(DC) _(—) _(DB8)=DC link voltage in brake mode at throttle level 8

V_(DC)=DC link voltage

P_(DC)=electrical power produced by a motor

R_(eff)=nominal per-inverter grid resistance

R_(base)=nominal per-inverter grid resistance at throttle level 8

η=motor efficiency

K=a motor constant

Flux linkage (λ) is defined in equation (1):

$\begin{matrix}{\lambda = {K \cdot \frac{V_{DC}}{\omega_{\varepsilon}}}} & (1)\end{matrix}$

By definition:

$\begin{matrix}{{V_{DC} = {K \cdot \frac{\sqrt{R_{eff} \cdot P_{DC}}}{\omega_{ɛ}}}}{and}} & (2) \\{P_{DC} = {\eta \cdot T_{ɛ} \cdot \omega_{m}}} & (3) \\{{\therefore\lambda} = {K \cdot \frac{\sqrt{R_{eff} \cdot \eta \cdot T_{ɛ} \cdot \omega_{m}}}{\omega_{ɛ}}}} & (4)\end{matrix}$

Referring briefly to FIG. 2, for a given motor configuration, aconsistent set of values may be ascertained involving a well-understoodmotor operating point. That condition is characterized with anindividual motor 24 in drive mode at the transition point betweenconstant torque operation and constant power operation with the throttleat maximum, known as throttle level 8. The transition point is referredto as “the knee” and occurs at a motor frequency of ω_(mc). FIG. 2illustrates a graph 60 of speed vs. power and shows the knee at thetransition between constant torque and constant power.

Feed-Forward Term

A feed forward power scale factor may be used to modify a base fluxestimate that accounts for flux variations based on motor state. Theactual value varies based on whether the motor is operating the constantpower or constant torque region.

When operating in the constant power region, the power scale factor maybe calculated as a ratio a current flux linkage divided by a nominalflux linkage at the knee.

$\begin{matrix}{\frac{\lambda}{\lambda_{o}} = {\frac{K \cdot \frac{\sqrt{R_{eff} \cdot \eta \cdot T_{ɛ} \cdot \omega_{m}}}{\omega_{ɛ}}}{K \cdot \frac{\sqrt{R_{eff} \cdot \eta \cdot T_{ɛ\; 8} \cdot \omega_{mc}}}{\omega_{ɛ}}} = \sqrt{\frac{T_{ɛ} \cdot \omega_{m}}{T_{ɛ\; 8} \cdot \omega_{mc}}}}} & (5)\end{matrix}$

For operation in the constant torque region, where the modulation ratiois not maximized and fixed, the motor frequency terms can be ignored andthe torque scale factor is represented by equation 6.

$\begin{matrix}{\frac{\lambda}{\lambda_{O}} = \sqrt{\frac{T_{ɛ}}{T_{ɛ\; 8}}}} & (6)\end{matrix}$

To account for changes in the DC link voltage between drive and brakemodes, a brake factor may be calculated. Referring to equation 7, below,the power of the motor in propel mode at the knee and the power in brakemode at the knee is related by the square of the ratio of the voltage ineach condition.

$\begin{matrix}{{T_{ɛ8} \cdot \omega_{mc}} = {T_{{DB}\; 8} \cdot \omega_{mc} \cdot \left( \frac{V_{{DC\_ TH}\; 8}}{V_{{DC\_ DB}\; 8}} \right)^{2}}} & (7)\end{matrix}$

Therefore, a brake factor constant may be developed as:

$\begin{matrix}\left( \frac{V_{{DC\_ TH}\; 8}}{V_{{DC\_ DB}\; 8}} \right)^{2} & (8)\end{matrix}$

Feedback Term

Last, using an effective resistance, that is, a resistance seen at theinverter, the impact of DC link voltage changes caused by wheel slip orinverter cut out may be accounted for.

First, observing the relationship between power in drive mode vs. brakemode, equation 7 may be used to modify equation 5, to develop theresistance scale factor of equation 9.

$\begin{matrix}\begin{matrix}{{{Resistance}\mspace{14mu} {Scale}\mspace{14mu} {Factor}} = \frac{\lambda}{\lambda_{o}}} \\{= \frac{K \cdot \sqrt{\frac{R_{eff} \cdot \eta \cdot T_{ɛ} \cdot \omega_{m}}{\omega_{ɛ}}}}{K \cdot \frac{\sqrt{R_{base} \cdot \eta \cdot R_{ɛ\; 8} \cdot \omega_{mc}}}{\omega_{ɛ}}}} \\{= \sqrt{\frac{R_{eff}}{R_{base}}}}\end{matrix} & (9)\end{matrix}$

In a purely electrical environment, power is defined as P=I²·R whereI=current and R is resistance. However, in the AC motor environment ofan exemplary embodiment, motor current is not measured, primarilybecause of the impact of placing a current sensor in the drive circuit.An alternate form of the power equation is

${P = \frac{V^{2}}{R}},$

where V is voltage, and therefore,

$R = {\frac{V^{2}}{P}.}$

Advantageously, the power of the motor 24 may be calculated from theknown quantities torque and motor frequency. A base resistanceassociated with throttle level 8 conditions may be calculated and usedas a constant, see, e.g., equation 10. The effective resistance can alsobe determined using the measured voltage and motor frequency, asillustrated in equation 11.

$\begin{matrix}{R_{base} = \frac{V_{{DC\_ DB}\; 8}^{2}}{\eta \cdot T_{{DB}\; 8} \cdot \omega_{m}}} & (10) \\{R_{eff} = \frac{V_{DC}^{2}}{\eta \cdot T_{{DB}\; 8} \cdot \omega_{m}}} & (11)\end{matrix}$

The resistance scale factor may then be restated in terms of parametersavailable to the controller 30 and the constant R_(base). Even thoughelectrical power is related to motor power by a motor efficiency factorη (see, e.g., equation 3 above), by assuming that motor efficiency isconstant, the motor efficiency term drops out of the following equation.

$\begin{matrix}{{{Resistance}\mspace{14mu} {Scale}\mspace{14mu} {Factor}} = {\sqrt{\frac{R_{eff}}{R_{base}}} = \sqrt{\frac{V_{DC}^{2}/\left( {T_{ɛ} \cdot \omega_{m}} \right)}{R_{base}}}}} & (12)\end{matrix}$

At very low speeds, where it is expected that the DC link voltage willbe supported solely by the generator 12, the resistance scale factor maybe clamped to unity.

CONCLUSION

The use of the brake factor, the resistance factor, and either the powerfactor or torque factor accommodate flux estimation for each operatingcondition as follows:

For normal balanced loading, with all inverters online and all gridpaths active: the resistance scale factor is unity and either the powerscale factor or the torque scale factor adjust a nominal flux value tofollow DC link voltage, where the appropriate scale factor is selectedbased on motor operating point.

For balanced loading with one inverter cut out and all grid pathsactive: with fewer inverters producing power, a normal torque request toan inverter will result in less total system power and lower DC linkvoltage. In this situation the resistance scale factor is less than one,providing the desired reduction in flux to correspond to the lower DClink voltage for the normal torque request.

For balanced loading with two inverters cut out and one grid pathactive: in this situation there are more inverters active per grid paththan normal, so a normal torque request to each inverter results in ahigher-than-normal DC link voltage. As a result, the resistance scalefactor is greater than one, providing the desired increase in fluxreference to correspond to the higher DC link voltage for the normaltorque request.

For all inverters online, with different loading between all invertersdue to, for example, wheel slip: for the light-loading inverters the DClink voltage will appear artificially high, which will cause theresistance scale factor to go up, boosting flux appropriately to matchthe available voltage; and for the heavier-loading inverters the DC linkvoltage will appear artificially low, which will cause the resistancescale factor to go down, cutting flux to match the available voltage.

OTHER EMBODIMENTS

In bogie control applications where each inverter operates with anisolated DC links, the torque reference is all that is needed for fluxestimation because there is a one-to-one relationship of torque andspeed to DC link voltage. On a bogie control locomotive withnon-isolated DC links there are two inverters and two grid paths so thatif one inverter is cut out one grid path is also disabled. So, theinstant system and method will address normal and inverter cut outoperation. However, the disclosed system may not properly account fornon-isolated DC link bogie control situation where both inverters areonline but not equally loaded, such as when one inverter is unloaded dueto wheel slip.

FIG. 3 illustrates a method 70 of adjusting application of electricalpower in a motor drive system 10 using an AC motor 24 driven by aninverter 22 that is coupled to a resistive grid 26 during retardoperation.

At a block 72, a braking factor may be calculated as a ratio of anominal power DC voltage vs. a nominal brake DC voltage, see, e.g.,equation 8.

A base resistance constant may also be calculated using characteristicsof the motor 24 at a first motor rotation frequency, where the firstmotor rotation frequency defines a transition between a constant torqueoperation of the motor 24 and a constant power operation of the motor 24(“the knee frequency”), see, e.g., equation 10. Further, a voltageconstant may be calculated as a ratio between a DC link voltage in apropel mode at throttle level 8 at the knee frequency and a DC linkvoltage in a brake mode at throttle level 8 at the knee frequency, see,e.g. equation 7.

At a block 74, a motor power may be calculated as a function of theactual torque and an actual motor rotation frequency, see, e.g.,equation 3.

At a block 76, a resistance scale factor may be calculated as a ratio ofmeasured grid effective resistance vs. a base grid resistance, where theeffective resistance at the inverter is a function of motor power and aDC link voltage, see, e.g., equation 11.

At a block 78, a determination may be made that motor operation is ineither a constant power region or a constant torque region as describedabove with respect to FIG. 2. In general, this determination may be madeby the controller 30 based on motor frequency using known motorcharacteristics and the controller's knowledge of a current operatingcondition of the motor 20.

When motor operation is in a constant power region, execution maycontinue at a block 80 where a nominal flux estimate may be multipliedwith a DC link voltage, the braking factor, the resistance scale factor,and a power scale factor to generate an adjusted flux estimate. Asdiscussed above, the resistance scale factor is a function of theeffective resistance and the base resistance constant, see, e.g.,equation 11 and the power scale factor is a function of a measuredtorque times mechanical frequency, see, e.g., equation 5.

At a block 82, inverter operation may be set to adjust motor torquebased on the adjusted flux estimate.

When, at block 78, motor operation is in a constant torque region,execution may continue at a block 84, where a nominal flux estimate maybe multiplied with a DC link voltage, the braking factor, the resistancescale factor, and a torque scale factor to generate an adjusted fluxestimate. The torque scale factor is a function of a measured torque,see, e.g., equation 6. Execution may then continue at block 82 asdescribed above.

From the block 82, the process may continue by returning to the block 74and proceeding as described above.

INDUSTRIAL APPLICABILITY

In general, applications using AC motors driven by inverters may benefitfrom the techniques described above. More particularly, railroadlocomotives using individual axle control or bogie control withnon-isolated DC links may see an increase in efficiency and powercontrol accuracy as a result of improved flux estimation, particularlyduring braking. Because locomotives are subject to unpredictablereal-world situations such as inverter cut-out and wheel slip, theability to arrive at a correct flux estimate provides a level of controlnot found in the prior art.

The current increase in commercial railroad traffic combined withongoing efforts to improve efficiency and environmental friendlinesscreate a climate where motor torque management and therefore the controlof motor power output are at a premium. The flux estimation techniquesdescribed above provide an additional resource for use in meeting thesedemands.

What is claimed is:
 1. A method of adjusting electrical powerapplication in a motor control system using an AC motor driven by aninverter bank that is coupled to a resistive grid during retardoperation, the method comprising: calculating a braking factor as aratio of a nominal power DC voltage vs. a nominal brake DC voltage;calculating a resistance scale factor as a ratio of measured gridresistance vs. a base grid resistance; determining that motor operationis in one of a constant power region or a constant torque region;multiplying a DC link voltage, the braking factor, the resistance scalefactor and one of a power scale factor when in a constant power regionor a torque scale factor when in a constant torque region to generate anadjusted flux estimate; and setting inverter operation to adjust motortorque based on the adjusted flux estimate, wherein the power scalefactor is a function of a measured torque times mechanical frequency vs.a characteristic torque times a corner point mechanical frequency andthe torque scale factor is a function of the measured torque vs. thecharacteristic torque.
 2. The method of claim 1, wherein the brakingfactor is calculated as$\left( \frac{V_{{DC\_ TH}\; 8}}{V_{{DC\_ DB}\; 8}} \right)^{2},$where V_(DC) _(—) _(TH8)=DC link voltage in propel mode at throttlelevel 8, and V_(DC) _(—) _(TH8)=DC link voltage in brake mode atthrottle level
 8. 3. The method of claim 1, wherein the resistance scalefactor is calculated as$\sqrt{\frac{V_{DC}^{2}/\left( {T_{ɛ} \cdot \omega_{m}} \right)}{V_{{DC\_ DB}\; 8}^{2}/\left( {T_{{DB}\; 8} \cdot \omega_{m}} \right)},}$where T_(ε)=torque of the motor, T_(DB8)=torque of the motor duringdynamic braking at throttle level 8, ω_(m)=mechanical frequency of themotor, V_(DC) _(—) _(DB8)=DC link voltage in brake mode at throttlelevel 8 and V_(DC)=DC link voltage.
 4. The method of claim 1, whereinthe power scale factor is calculated as$\sqrt{\frac{T_{ɛ} \cdot \omega_{m}}{T_{ɛ\; 8} \cdot \omega_{m\; c}}},$where T_(ε8)=torque of the motor at throttle level 8, T_(ε)=torque ofthe motor, ω_(m)=mechanical frequency of the motor, ω_(mc)=mechanicalfrequency of the motor at a knee frequency defined at a transition pointbetween constant torque operation of the motor and constant poweroperation of the motor.
 5. The method of claim 1, wherein the torquescale factor is calculated as $\sqrt{\frac{T_{ɛ}}{T_{ɛ\; 8}}},$ whereT_(ε8)=torque of the motor at throttle level 8, T_(ε)=torque of themotor.
 6. The method of claim 2, wherein the resistance scale factor iscalculated as a square root of effective resistance divided by a baseresistance defined by the equation:$\sqrt{\frac{V_{DC}^{2}/\left( {T_{ɛ} \cdot \omega_{m}} \right)}{V_{{DC\_ DB}\; 8}^{2}/\left( {T_{{DB}\; 8} \cdot \omega_{m\; c}} \right)},}$where T_(ε)=torque of the motor, T_(DB8)=torque of the motor duringdynamic braking at throttle level 8, ω_(m)=mechanical frequency of themotor, ω_(mc)=mechanical frequency of the motor at a knee frequencydefined at a transition point between constant torque operation of themotor and constant power operation of the motor, V_(DC) _(—) _(DB8)=DClink voltage in brake mode at throttle level 8 and V_(DC)=DC linkvoltage.
 7. The method of claim 6, wherein the power scale factor iscalculated as$\sqrt{\frac{T_{ɛ} \cdot \omega_{m}}{T_{ɛ\; 8} \cdot \omega_{m\; c}}},$where T_(ε8)=torque of the motor at throttle level
 8. 8. The method ofclaim 7, wherein the torque scale factor is calculated as$\sqrt{\frac{T_{ɛ}}{T_{ɛ\; 8}}}.$
 9. A method of operating an AC motordriven by an inverter, the method comprising: determining a baseresistance constant using characteristics of the motor at a first motorrotation frequency, the first motor rotation frequency defined at atransition point between constant torque operation of the motor andconstant power operation of the motor (“the knee frequency”);calculating motor power as a function of the actual torque and theactual motor rotation frequency; calculating an effective resistance atthe inverter as a function of motor power and a voltage on the DC link;calculating an estimated flux reference as a function of the DC linkvoltage, the effective resistance, and the base resistance constant; andadjusting torque output of the motor based on the estimated fluxreference.
 10. The method of claim 9, further comprising: calculating avoltage constant as a ratio between a DC link voltage in a propel modeat throttle level 8 at the knee frequency and a DC link voltage in abrake mode at throttle level 8 at the knee frequency, whereincalculating the estimated flux reference includes calculating theestimated flux reference as a further function of the voltage constant.11. The method of claim 10, further comprising: determining that the ACmotor is operating in a constant power region; and calculating a firstscaling factor when the motor operation is in the constant torqueregion, wherein calculating the estimated flux reference includescalculating the estimated flux reference as a further function of thefirst scaling factor.
 12. The method of claim 11, wherein calculatingthe first scaling factor comprises calculating$\sqrt{\frac{T_{ɛ} \cdot \omega_{m}}{T_{ɛ\; 8} \cdot \omega_{m\; c}}},$where T_(ε)=torque of the motor, T_(ε8)=torque of the motor at throttlelevel 8, ω_(m)=mechanical frequency of the motor, ω_(mc)=the kneefrequency.
 13. The method of claim 10, further comprising: determiningthat the AC motor is operating in a constant torque region; andcalculating a second scaling factor when the motor operation is in theconstant torque region, wherein calculating the estimated flux referenceincludes calculating the estimated flux reference as a further functionof the second scaling factor.
 14. The method of claim 13, whereincalculating the second scaling factor comprises calculating$\sqrt{\frac{T_{ɛ}}{T_{ɛ\; 8}}}.$
 15. The method of claim 14, whereindetermining the base resistance constant comprises: determining a valuefor V_(DC) _(—) _(DB8)=DC link voltage in brake mode at throttle level8; determining a value for T_(DB8)=torque of the motor during dynamicbraking at throttle level 8; determining a value for ω_(mc)=mechanicalfrequency of the motor at the knee frequency, and calculating the baseresistance constant as R_(base)=V_(DC) _(—) _(DB8) ²/η·T_(DB8)·ω_(m).16. The method of claim 15, wherein calculating the effective resistancecomprises calculating$\sqrt{\frac{V_{DC}^{2}/\left( {T_{ɛ} \cdot \omega_{m}} \right)}{R_{base}}}.$17. An alternating current (AC) motor system adapted to adjust motorflux based on motor power, a direct current (DC) link voltage and aneffective resistance at an inverter used to drive the AC motor, thesystem comprising: an AC generator; a rectifier that converts an outputof the generator to DC power; a DC link coupled to the rectifier; aresistive grid selectively coupled to the DC link; a plurality of ACmotors; a plurality of inverters, each of the plurality of inverterselectrically coupling the DC link to a respective one AC motor of theplurality of AC motors; a controller coupled to the DC link, theresistive grid, and each of the plurality of inverters, the controllerincluding: a processor; and a memory storing instructions that whenexecuted on the processor cause the controller to: calculate anestimated flux based at least in part on an effective resistance of thegrid at each inverter of the plurality of inverters, the effectiveresistance calculated from actual torque, actual motor rotationfrequency, the DC link voltage and a base resistance constant; andadjust a setting for each inverter of the plurality of inverters thatcontrols a torque of the AC motor associated with each inverter.
 18. TheAC motor system of claim 17, wherein the memory stores furtherinstructions that when executed on the processor cause the controllerto: calculate a resistance scale factor based on the effectiveresistance the resistance scale factor defined as$\sqrt{\frac{V_{DC}^{2}/\left( {T_{ɛ} \cdot \omega_{m}} \right)}{V_{{DC\_ DB}\; 8}^{2}/\left( {T_{{DB}\; 8} \cdot \omega_{m}} \right)},}$where T_(ε)=torque of the motor, T_(DB8)=torque of the motor duringdynamic braking at throttle level 8, ω_(m)=mechanical frequency of themotor, V_(DC) _(—) _(DB8)=DC link voltage in brake mode at throttlelevel 8, and V_(DC)=DC link voltage, the resistance scale factor used tocalculate the estimated flux.
 19. The AC motor system of claim 17,wherein the memory stores further instructions that when executed on theprocessor cause the controller to: use an additional factor to calculatethe estimated flux defined as a power scale factor calculated as$\sqrt{\frac{T_{ɛ} \cdot \omega_{m}}{T_{ɛ\; 8} \cdot \omega_{m\; c}}},$where T_(ε8)=torque of the motor at throttle level 8, T_(ε)=torque ofthe motor, ω_(m)=mechanical frequency of the motor, ω_(mc)=mechanicalfrequency of the motor at a knee frequency defined at a transition pointbetween constant torque operation of the motor and constant poweroperation of the motor, the power scale factor used when the AC motor isin a constant power region of operation.
 20. The AC motor system ofclaim 17, wherein the memory stores further instructions that whenexecuted on the processor cause the controller to: use an additionalfactor to calculate the estimated flux defined as a torque scale factorcalculated as $\sqrt{\frac{T_{ɛ}}{T_{ɛ\; 8}}},$ where T_(ε8)=torque ofthe motor at throttle level 8, T_(ε)=torque of the motor,ω_(m)=mechanical frequency of the motor, the torque scale factor usedwhen the AC motor is in a constant torque region of operation.